Laser absorption spectroscopy isotopic gas analyzer

ABSTRACT

The present invention provides systems and methods for measuring the isotope ratios of one or more trace gases based on optical absorption spectroscopy methods. The system includes an optical cavity containing a gas. The system also includes a laser optically coupled with the optical cavity, and a detector system for measuring absorption of laser light by the gas in the cavity.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims the benefit of, and priority to, U.S.provisional Patent application No. 62/535,505 filed on Jul. 21, 2017 thecontents of which are hereby incorporated by reference.

BACKGROUND OF THE INVENTION

The present invention relates generally to trace gas detection and morespecifically to laser absorption spectroscopy systems and methods.

Optical absorption spectroscopy involves passing radiation through asample, e.g., an analyte and measuring absorption property of the sampleas a function of the radiation wavelength. For example, trace gasdetection can be spectroscopically performed by taking measurements todetect the presence or absence of spectral absorption linescorresponding to the gas species of interest. Trace gas detection can bespectroscopically performed by taking measurements to quantify spectralabsorption lines corresponding to the gas species of interest and tocompute concentrations of analytes, gas pressure, and gas temperature.Spectroscopic analysis of isotopologues can also be performed. However,because the integral line intensities of absorption gas lines aresensitive to the gas temperature, and the line shapes of those lines aresensitive to the gas temperature, the gas pressure, and the gascomposition, measurements of the isotopic ratio with high accuracyrequire highly accurate measurements of the analyzed gas temperature andpressure. In addition, such measurements of the integral intensities ofdifferent lines also require very precise measurements of laserfrequency. Moreover, because the natural abundance for isotopes can bevery different, the integral line intensities of absorption gas lines ofdifferent isotopologues can also be very different, because the integralintensities are the products of the line strengths, gas concentrationand isotpologue abundance. That is why it might be hard to preciselymeasure the integral intensities of the absorption lines of lessabundant isotopologues and as a result of that to precisely measure theratio of concentrations of two isotopologues with quite differentabundances.

Accordingly it is desirable to provide improved spectroscopy systems andmethods for measuring concentrations of different isotopologues in theirgas phase.

BRIEF SUMMARY OF THE INVENTION

The present invention provides systems and methods for measuring theisotope ratios of one or more trace gases.

Embodiments of the present invention provide systems and devices fordetecting the isotopic ratios of the analyzed gas with high accuracyusing an optical cavity, which contains a gas mixture to be analyzed,one or more lasers coupled to one or more cavities, and one or morelight sensitive detectors. The optical cavity can be a resonant opticalcavity. The resonant cavity can be any type of cavity with two or morecavity mirrors, including a linear or a ring cavity. A laser that iscapable of being frequency-scanned can be coupled to the cavity thoughone of the cavity mirrors. A detection method can be based on any of avariety of cavity enhanced optical spectroscopy (CEOS) methods, forexample, cavity ring-down spectroscopy (CRDS) methods, cavity phaseshift spectroscopy methods, cavity enhanced absorption spectroscopy(CEAS) methods, integrated cavity output spectroscopy (ICOS), or cavityenhanced photo-acoustic spectroscopy (CE-PAS) methods. A detectionmethod can also be based on tunable diode laser absorption spectroscopy(TDLAS) methods with or without using a multipass cell. Photo-acousticspectroscopy (PAS) can also be used as a detection method.

The approach of one embodiment is based on the fact that spectral lineintensities of different rotational-vibrational bands of an isotopologuecan be quite different and different rotational-vibrational bands mayoccupy different spectral regions. FIGS. 1-5 show line intensities ofdifferent rotational-vibrational transitions for differentrotational-vibrational bands for ¹²C¹⁶O₂ isotopologue, where “T” is theabsolute temperature of the gas. So, it may be preferable to measurestrong rotational-vibrational bands of the less abundant isotopologue inone spectral region and weak rotational-vibrational bands of the moreabundant isotopologue in another spectral region.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

FIG. 1. Line intensities of different rotational-vibrational transitionsfrom one rotational level in the ground vibrational state to onerotational level in the vibrationally excited state v₃ of ¹²C¹⁶O₂isotopologue at 296 K.

FIG. 2. Line intensities of different rotational-vibrational transitionsfrom one rotational level in the ground vibrational state to onerotational level in the vibrationally excited state v₁+v₃ of ¹²C¹⁶O₂isotopologue at 296 K.

FIG. 3. Line intensities of different rotational-vibrational transitionsfrom one rotational level in the ground vibrational state to onerotational level in the vibrationally excited state v₁+2v₂+v₃ of ¹²C¹⁶O₂isotopologue at 296 K.

FIG. 4. Line intensities of different rotational-vibrational transitionsfrom one rotational level in the ground vibrational state to onerotational level in the vibrationally excited state v₁+4v₂+v₃ of ¹²C¹⁶O₂isotopologue at 296 K.

FIG. 5. Line intensities of different rotational-vibrational transitionsfrom one rotational level in the ground vibrational state to onerotational level in the vibrationally excited state 2v₁+2v₂+v₃ of¹²C¹⁶O₂ isotopologue at 296 K.

FIG. 6. Line intensities of different rotational-vibrational transitionsfrom one rotational level in the ground vibrational state to onerotational level in the vibrationally excited state v₃ of ¹³C¹⁶O₂isotopologue at 296 K.

FIG. 7. Line intensities of different rotational-vibrational transitionsfrom one rotational level in the ground vibrational state to onerotational level in the vibrationally excited state v₁+v₃ of ¹³C¹⁶O₂isotopologue at 296 K.

FIG. 8. Line intensities of different rotational-vibrational transitionsfrom one rotational level in the ground vibrational state to onerotational level in the vibrationally excited state v₁+2v₂+v₃ of ¹³C¹⁶O₂isotopologue at 296 K.

FIG. 9. Line intensities of different rotational-vibrational transitionsfrom one rotational level in the ground vibrational state to onerotational level in the vibrationally excited state v₁+4v₂+v₃ of ¹³C¹⁶O₂isotopologue at 296 K.

FIG. 10. Line intensities of different rotational-vibrationaltransitions from one rotational level in the ground vibrational state toone rotational level in the vibrationally excited state 2v₁+2v₂+v₃ of¹³C¹⁶O₂ isotopologue at 296 K.

FIG. 11. The ratio of the spectrum of the ¹³C¹⁶O₂ isotopologue to thesum of spectra of all other isopologues of CO₂ from 2040.5 nm to 2043 nmat a pressure of 100 mBar and a temperature of 296 K. R_(x) symbols showpositions where the corresponding rotational-vibrational transitions,from one rotational level in the ground vibrational state to anotherrotational level in the vibrationally excited state v₁+2v₂+v₃ of ¹³C¹⁶O₂isotopologue, are located.

FIG. 12. The ratio of the spectrum of the ¹³C¹⁶O₂ isotopologue to thesum of spectra of all isopologues of water from 2040.5 nm to 2043 nm ata pressure of 100 mBar and a temperature of 296 K. R_(N) symbols showpositions where the corresponding rotational-vibrational transitions,from one rotational level in the ground vibrational state to anotherrotational level in the vibrationally excited state v₁+2v₂+v₃ of ¹³C¹⁶O₂isotopologue, are located.

FIG. 13. The ratio of the spectrum of the ¹³C¹⁶O₂ isotopologue to thesum of spectra of all isopologues of methane from 2040.5 nm to 2043 nmat a pressure of 100 mBar and a temperature of 296 K. R_(N) symbols showpositions where the corresponding rotational-vibrational transitions,from one rotational level in the ground vibrational state to anotherrotational level in the vibrationally excited state v₁+2v₂+v₃ of ¹³C¹⁶O₂isotopologue, are located.

FIG. 14. The ratio of the spectrum of the ¹²C¹⁶O₂ isotopologue to thesum of spectra of all other isopologues of CO₂ from 1572.5 nm to 1575 nmat a pressure of 100 mBar and a temperature of 296 K. R_(x) symbols showpositions where the corresponding rotational-vibrational transitions,from one rotational level in the ground vibrational state to anotherrotational level in the vibrationally excited state 2v₁+2v₂+v₃ of¹³C¹⁶O₂ isotopologue, are located.

FIG. 15. The ratio of the spectrum of the ¹²C¹⁶O₂ isotopologue to thesum of spectra of all isopologues of water from 1572.5 nm to 1575 nm ata pressure of 100 mBar and a temperature of 296 K. R_(x) symbols showpositions where the corresponding rotational-vibrational transitions,from one rotational level in the ground vibrational state to anotherrotational level in the vibrationally excited state 2v₁+2v₂+v₃ of¹³C¹⁶O₂ isotopologue, are located.

FIG. 16. The ratio of the spectrum of the ¹²C¹⁶O₂ isotopologue to thesum of spectra of all isopologues of methane from 1572.5 nm to 1575 nmat a pressure of 100 mBar and a temperature of 296 K. R_(x) symbols showpositions where the corresponding rotational-vibrational transitions,from one rotational level in the ground vibrational state to anotherrotational level in the vibrationally excited state 2v₁+2v₂+v₃ of¹³C¹⁶O₂ isotopologue, are located.

FIG. 17. Spectrum of the ¹³C¹⁶O₂ isotopologue, the sum of spectra of allother isopologues of CO₂, and the sum of spectra of all isopologues ofwater from 2040.5 nm to 2043 nm at a pressure of 100 mBar and atemperature of 296 K. R_(x) symbols show positions where thecorresponding rotational-vibrational transitions, from one rotationallevel in the ground vibrational state to another rotational level in thevibrationally excited state v₁+2v₂+v₃ of ¹³C¹⁶O₂ isotopologue, arelocated. The total concentration of carbon dioxide is 400 part permillion. The total concentration of water is 1%.

FIG. 18. Spectrum of the ¹²C¹⁶O₂ isotopologue, the sum of spectra of allother isopologues of CO₂, the sum of spectra of all isopologues ofwater, and the sum of spectra of all isopologues of methane from 1572.5nm to 1575 nm at a pressure of 100 mBar and a temperature of 296 K.R_(x) symbols show positions where corresponding rotational-vibrationaltransitions from one rotational level in the ground vibrational state toanother rotational level in the vibrationally excited state 2v₁+2v₂+v₃of ¹³C¹⁶O₂ isotopologue are located. The total concentration of carbondioxide is 400 part per million. The total concentration of water is 1%.

DETAILED DESCRIPTION OF THE INVENTION

Here and further we use the term “the spectral line intensity” in unitsof [cm⁻¹/(molecule cm⁻²)] similar to what was given in FIG. 1 in theAppendix to the article on the 1996 Edition of HITRAN in the Journal ofQuantitative Spectroscopy and Radiative Transfer vol. 60, pp. 665-710(1998). However, in our case the spectral line intensities are specifiedper an isotopologue molecule, while the spectral line intensities thatappear in HITRAN are weighted according to the natural terrestrialisotopic abundances.

Systems and methods described herein may include or employ one or morespectrometers measuring rotational-vibrational spectra of differentisotolologues in the gas phase. The rotational-vibrational spectra areoften resolved into lines due to transitions from one rotational levelin the ground vibrational state to one rotational level in thevibrationally excited state. The lines corresponding to a givenvibrational transition form a band. The gas analyzer system measuresrotational-vibrational spectra of isotopologues in the gas phase atleast at two non-overlapping spectral regions: in a first spectralregion the system measures at least one rotational-vibrational line of aless abundant isotopologue, and in a second spectral region the systemmeasures at least one rotational-vibrational line of a more abundantisotopologue. Other lines of other isotopologues and other chemicalspecies can also be measured in both spectral regions. To improve thesystem performance, these two lines belong to different vibrationalmodes chosen in such a way that the spectral line intensity of thestrongest rotational-vibrational line of the vibrational mode of theless abundant isotopologue is at least two or more times stronger thanthe spectral line intensity of the strongest rotational-vibrational lineof the vibrational mode of the more abundant isotopologue. This approachpermits to improve both the precision and the accuracy of the isotoperatio measurements because the line intensities of two measured linesmight be closer to each other, in comparison with the case when twolines of the same vibrational modes of two isotopologues are measured.Notice, in general, for spectral analysis one can chooserotational-vibrational lines with quite different spectral lineintensities from the same vibrational modes of different isotopologues.However, in that case these lines usually have quite different pressurebroadening and temperature dependences. So, the precise isotopic ratioanalysis would require extremely accurate temperature and pressurestabilizations of the tested gas.

FIGS. 1-10 show examples of the line intensities of differentvibrational modes of the two most abundant isotopologues of carbondioxide in Mid-IR and NIR-IR spectral regions. Circles representdifferent rotational-vibrational transitions from one rotational levelin the ground vibrational state to another rotational level in thevibrationally excited state. The line intensities were obtained from theHITRAN database. The energy change of rotation can be either subtractedfrom or added to the energy change of vibration, giving the P- andR-branches of the spectrum, respectively. Both P- and R branches areshown. Taking to account that abundance of carbon dioxide isopologues,according to HITAN is 98.42% and 1.106% for ¹²C¹⁶O₂ and ¹³C¹⁶O₂,respectively, the following pairs of rotational-vibrational bands can beconsidered for spectral analysis according to one of the embodiments:

-   -   1) v₁+v₃ vibrational mode of ¹²C¹⁶O₂ and v₃ vibrational mode of        ¹³C¹⁶O₂;    -   2) v₁+2v₂+v₃ vibrational mode of ¹²C¹⁶O₂ and v₃ vibrational mode        of ¹³C¹⁶O₂;    -   3) v₁+4v₂+v₃ vibrational mode of ¹²C¹⁶O₂ and v₃ vibrational mode        of ¹³C¹⁶O₂;    -   4) 2v₁+2v₂+v₃ vibrational mode of ¹²C¹⁶O₂ and v₃ vibrational        mode of ¹³C¹⁶O₂;    -   5) v₁+2v₂+v₃ vibrational mode of ¹²C¹⁶O₂ and v₁+v₃ vibrational        mode of ¹³C¹⁶O₂;    -   6) v₁+4v₂+v₃ vibrational mode of ¹²C¹⁶O₂ and v₁+v₃ vibrational        mode of ¹³C¹⁶O₂;    -   7) 2v₁+2v₂+v₃ mode of for ¹²C¹⁶O₂ and v₁+v₃ mode of ¹³C¹⁶O₂;    -   8) v₁+4v₂+v₃ vibrational mode of ¹²C¹⁶O₂ and v₁+2v₂+v₃        vibrational mode of ¹³C¹⁶O₂;    -   9) 2v₁+2v₂+v₃ vibrational mode of ¹²C¹⁶O₂ and v₁+2v₂+v₃        vibrational mode of ¹³C¹⁶O₂;        where v₁, v₂, and v₃ represent normal modes of the CO₂ molecule:        symmetric stretch, bend, and asymmetric stretch, respectively.

By comparing FIGS. 1-10 one can easily see that the bands in these pairsare spectrally well separated and the line intensity of the strongestline in the band of the less abundant isotopologue is at least as twiceas strong as the line intensity of the strongest line in the band of themore abandon isotopologue.

Line intensity is the integrated absorption cross section across a line.Because the line intensities are temperature dependent, the lineintensities of different lines should be compared at the temperature ofthe measured gas. The temperature dependence coefficient is defined as aderivative of the line intensity over temperature divided by the lineintensity itself. The temperature dependence coefficients depend ontemperature and according to one embodiment they are compared at thetemperature of a measured gas mixture.

After a pair of rotational-vibrational bands corresponding to twodifferent isotopologues was selected for spectral analysis, spectralranges for measuring the isotopologue concentration ratios can be chosenaccording to another embodiment: at least one of therotational-vibrational lines of the band of the less abundantisotopologue is located and measured in the first spectral region, andat least one of the rotational-vibrational lines of the band of the moreabundant isotopologue is located and measured in the second spectralregion.

According to another embodiment the ratio of an absorption spectrum ofthe less abundant isotopologue in the first selected spectral region tothe sum of the absorption spectra of all other isotopologues of the samechemical substance exceeds two somewhere in the first selected spectralregion, and the ratio of an absorption spectrum of the more abundantisotopologue in the second selected spectral region to the sum of theabsorption spectra of all other isotopologues of the same chemicalsubstance exceeds two somewhere in the second selected spectral region.These spectra are compared at the temperature and at the pressure of themeasured gas or gas mixture.

As an example, the rotational-vibrational band corresponding to the2v₁+2v₂+v₃ vibrational mode of ¹²C¹⁶O₂ and the rotational-vibrationalband corresponding to the v₁+2v₂+v₃ vibrational mode of ¹³C¹⁶O₂ areselected to illustrate the method. FIG. 11 shows the ratio of anabsorption spectrum of the less abundant isotopologue, ¹³C¹⁶O₂, in thefirst selected spectral region to the sum of the absorption spectra ofall other isotopologues of carbon dioxide at a pressure of 100 mBar andat a temperature of 296 K. FIG. 14 shows the ratio of an absorptionsspectrum of the more abundant isotopologue, ¹²C¹⁶O₂, in the secondselected spectral region to the sum of spectra of all otherisotopologues of carbon dioxide at a pressure of 100 mBar and at atemperature of 296 K. P stands for gas pressure. All figures from 11 to18 were created for gas pressure P=100 mBar, and gas temperature T=296K.S( ) is an absorption spectrum of a particular isotopologue. Σ standsfor sum, while indexes i, j, and k describe different isotopes ofhydrogen, oxygen, or carbon atoms. One can see that at some spectralpoints corresponding to some rotational-vibrational lines the ratiosexceed number two. The sums of spectra were calculated taking intoaccount the abundances of different isotopologues.

As another example, the R12 rotational-vibrational line of the v₁+2v₂+v₃vibrational mode of ¹³C¹⁶O₂ and the R10 rotational-vibrational line ofthe 2v₁+2v₂+v₃ vibrational mode of ¹²C¹⁶O₂ can be selected for isotopicratio analysis. The first spectral range to measure lines of ¹³C¹⁶O₂ isfrom 2040.5 nm to 2043 nm. The second spectral range to measure lines of¹²C¹⁶O₂ is from 1572.5 nm to 1575 nm. Notice, theserotational-vibrational lines correspond to quite different transitionsfrom one rotational level in the ground vibrational state to onerotational level in the vibrationally excited state. For example, theR12 rotational-vibrational line of the v₁+2v₂+v₃ vibrational mode of¹³C¹⁶O₂ corresponds to the transition (v₁=0, v₂=0, v₃=0, J=12)→(v₁=1,v₂=2, v₃=1, J=13) from the rotation level J=12 of the ground state tothe rotation level J=13 of the vibrationally excited v₁+2v₂+v₃vibrational mode, or to (Δv₁=+1, Δv₂=+2, Δv₁=+1, ΔJ=+1) transition,while the R10 rotational-vibrational line of 2v₁+2v₂+v₃ vibrational modeof ¹²C¹⁶O₂ corresponds to the transition (v₁=0, v₂=0, v₃=0, J=10)→(v₁=2,v₂=2, v₃=1, J=11) from the rotation level J=10 of the ground state tothe rotation level J=1 of the vibrationally excited 2v₁+2v₂+v₃vibrational mode, or to (Δv₁=+2, Δv₂=+2, Δv₁=+1, ΔJ=+1) transition.

According to a general convention rotational-vibrational bands can bedivided on three branches: R-branch, P-branch, and Q-branch:

-   -   R branch: when ΔJ=+1, i.e. the rotational quantum number in the        ground state is one more than the rotational quantum number in        the excited state;    -   P branch: when ΔJ=−1, i.e. the rotational quantum number in the        ground state is one less than the rotational quantum number in        the excited state;    -   Q branch: when ΔJ=0, i.e. the rotational quantum number in the        ground state is the same as the rotational quantum number in the        excited state.

The following tables show some parameters of the selected vibrationmodes of two isotpologues.

TABLE 1 v₁ + 2v₂ + v₃ band of ¹³C¹⁶O₂: branch symbol (P or R), J is thequantum number associated with the total angular momentum, wavelength λ[nm], line strength S [cm⁻¹/(molecule cm⁻²)], air-broadened half-widthγ_(air) [cm⁻¹ atm⁻¹], self-broadened half-width γ_(self) [cm⁻¹ atm⁻¹],and temperature dependence coefficient dS/SdT [K⁻¹]. J λ S γ_(air)γ_(self) dS/SdT P 38 2060.5951 2.14E−22 0.0681 0.083 5.17E−03 P 362059.7220 2.69E−22 0.0683 0.085 4.12E−03 P 34 2058.8614 3.32E−22 0.06850.087 3.34E−03 P 32 2058.0131 4.02E−22 0.0687 0.089 2.30E−03 P 302057.1772 4.78E−22 0.0690 0.091 1.55E−03 P 28 2056.3536 5.56E−22 0.06930.093 8.33E−04 P 26 2055.5421 6.36E−22 0.0699 0.094 1.46E−04 P 242054.7428 7.11E−22 0.0706 0.096 −5.22E−04 P 22 2053.9556 7.79E−22 0.07150.098 −1.19E−03 P 20 2053.1805 8.32E−22 0.0727 0.099 −1.68E−03 P 182052.4173 8.67E−22 0.0741 0.101 −2.15E−03 P 16 2051.6662 8.80E−22 0.07580.103 −2.64E−03 P 14 2050.9269 8.66E−22 0.0778 0.105 −3.01E−03 P 122050.1996 8.22E−22 0.0798 0.107 −3.40E−03 P 10 2049.4841 7.48E−22 0.08200.109 −3.62E−03 P 8 2048.7805 6.43E−22 0.0842 0.112 −3.91E−03 P 62048.0886 5.11E−22 0.0861 0.115 −4.02E−03 P 4 2047.4086 3.55E−22 0.08770.117 −4.20E−03 P 2 2046.7403 1.83E−22 0.0891 0.120 −4.09E−03 R 02045.7599 9.22E−23 0.0925 0.125 −4.34E−03 R 2 2045.1210 2.75E−22 0.08830.118 −4.42E−03 R 4 2044.4938 4.46E−22 0.0870 0.116 −4.18E−03 R 62043.8783 6.01E−22 0.0852 0.113 −4.04E−03 R 8 2043.2746 7.31E−22 0.08310.110 −3.96E−03 R 10 2042.6826 8.32E−22 0.0808 0.108 −3.70E−03 R 122042.1023 9.04E−22 0.0788 0.106 −3.40E−03 R 14 2041.5338 9.41E−22 0.07680.104 −2.96E−03 R 16 2040.9770 9.50E−22 0.0749 0.102 −2.93E−03 R 182040.4319 9.32E−22 0.0733 0.100 −1.99E−03 R 20 2039.8987 8.94E−22 0.07210.099 −1.66E−03 R 22 2039.3773 8.35E−22 0.0710 0.097 −1.11E−03 R 242038.8677 7.62E−22 0.0702 0.095 −4.88E−04 R 26 2038.3699 6.80E−22 0.06960.094 1.36E−04 R 28 2037.8841 5.95E−22 0.0691 0.092 7.79E−04 R 302037.4101 5.11E−22 0.0688 0.090 1.63E−03 R 32 2036.9481 4.30E−22 0.06860.088 2.37E−03 R 34 2036.4981 3.55E−22 0.0684 0.086 3.12E−03 R 362036.0600 2.88E−22 0.0682 0.084 4.17E−03 R 38 2035.6341 2.30E−22 0.06800.082 5.23E−03

TABLE 2 2v₁ + 2v₂ + v₃ band of ¹²C¹⁶O₂: branch symbol (P or R), J is thequantum number associated with the total angular momentum, wavelength λ[nm], line strength S [cm⁻¹/(molecule cm⁻²)], air-broadened half-widthγ_(air) [cm⁻¹ atm¹], self-broadened half- width γ_(self) [cm⁻¹ atm⁻¹],and temperature dependence coefficient dS/SdT [K⁻¹]. J λ S γ_(air)γ_(self) dS/SdT P 38 1584.0323 3.79E−24 0.0682 0.082 5.20E−03 P 361583.5076 4.80E−24 0.0686 0.084 4.10E−03 P 34 1582.9901 5.97E−24 0.06890.086 3.30E−03 P 32 1582.4799 7.28E−24 0.0695 0.088 2.42E−03 P 301581.9770 8.71E−24 0.0698 0.090 1.67E−03 P 28 1581.4815 1.02E−23 0.07030.092 9.13E−04 P 26 1580.9933 1.18E−23 0.0709 0.094 0.00E+00 P 241580.5127 1.32E−23 0.0716 0.096 −7.84E−04 P 22 1580.0395 1.45E−23 0.07270.098 −1.43E−03 P 20 1579.5739 1.56E−23 0.0741 0.100 −1.33E−03 P 181579.1158 1.64E−23 0.0749 0.101 −1.90E−03 P 16 1578.6654 1.67E−23 0.07660.104 −2.49E−03 P 14 1578.2224 1.65E−23 0.0781 0.105 −3.15E−03 P 121577.7872 1.57E−23 0.0797 0.108 −3.31E−03 P 10 1577.3596 1.43E−23 0.08130.109 −3.63E−03 P 8 1576.9396 1.23E−23 0.0830 0.112 −4.21E−03 P 61576.5273 9.80E−24 0.0854 0.115 −4.02E−03 P 4 1576.1226 6.82E−24 0.08730.118 −4.10E−03 P 2 1575.7256 3.51E−24 0.0920 0.123 −4.14E−03 R 01575.1445 1.78E−24 0.0953 0.129 −4.08E−03 R 2 1574.7667 5.28E−24 0.08840.120 −4.32E−03 R 4 1574.3965 8.58E−24 0.0858 0.116 −4.11E−03 R 61574.0340 1.15E−23 0.0838 0.114 −3.60E−03 R 8 1573.6790 1.40E−23 0.08160.111 −3.70E−03 R 10 1573.3317 1.59E−23 0.0800 0.108 −3.91E−03 R 121572.9920 1.72E−23 0.0781 0.106 −3.01E−03 R 14 1572.6598 1.80E−23 0.07660.104 −2.89E−03 R 16 1572.3352 1.81E−23 0.0747 0.102 −2.29E−03 R 181572.0180 1.77E−23 0.0738 0.100 −2.35E−03 R 20 1571.7083 1.68E−23 0.07270.098 −1.85E−03 R 22 1571.4060 1.56E−23 0.0718 0.097 −1.33E−03 R 241571.1112 1.42E−23 0.0710 0.095 −7.30E−04 R 26 1570.8236 1.26E−23 0.07030.093 0.00E+00 R 28 1570.5434 1.10E−23 0.0700 0.091 9.44E−04 R 301570.2704 9.35E−24 0.0694 0.089 1.66E−03 R 32 1570.0046 7.82E−24 0.06890.087 2.39E−03 R 34 1569.7459 6.41E−24 0.0685 0.085 3.23E−03 R 361569.4943 5.16E−24 0.0689 0.084 4.21E−03 R 38 1569.2497 4.08E−24 0.06790.081 5.08E−03

Table 1 and Table 2 show that both selected lines (R12rotational-vibrational line of v₁+2v₂+v₃ vibrational mode of ¹³C¹⁶O₂ andR10 rotational-vibrational line of 2v₁+2v₂+v₃ vibrational mode) satisfyto another embodiment: the pressure broadening coefficients of theselines are different by no more than 50%.

Table 1 and Table 2 also show that both selected lines (R12rotational-vibrational line of v₁+2v₂+v₃ vibrational mode of ¹³C¹⁶O₂ andR10 rotational-vibrational line of 2v₁+2v₂+v₃ vibrational mode) satisfyyet to another embodiment: the temperature dependence coefficients ofthese lines are different by no more than 50%.

If other inference species are present in the gas or in the mixture,similar spectral analysis may help better choose spectral regions. FIG.12 and FIG. 13 show the ratios of the absorption spectrum of ¹³C¹⁶O₂ inthe first selected spectral region to the sum of absorption spectra ofall water isotopologues and to the sum of absorption spectra of allmethane isotopologues at a pressure of 100 mBar and at a temperature of296 K. FIG. 15 and FIG. 16 show the ratios of the absorption spectrum of¹²C¹⁶O₂ in the second selected spectral region to the sum of absorptionspectra of all H₂O isotopologues and to the sum of absorption spectra ofall CH₄ isotopologues at a pressure of 100 mBar and at a temperature of296 K. Concentrations of CO₂, H₂O, and CH₄ in FIGS. 12-16 are the same.The sums were calculated taking into account abundances of differentisotopologues.

FIG. 17 and FIG. 18 show simulated absorptions spectra at two selectedspectral regions. These figures show that by choosingrotational-vibrational lines which belong to different bands indifferent spectral regions, the instrument accuracy can be significantlyimproved: the analytical lines are not only relatively spectrally clean,but they also have close absorption coefficients and very close pressurebroadening parameters and temperature dependencies. The first conditionspermit to optimize the measurement method for both isotopologues. Thelast two conditions make these measurement less affected by both thepressure and temperature uncertainties.

According to another embodiment, a gas analyzer system is provided formeasuring an isotopic ratio gas species. The system typically includes aresonant optical cavity having two or more mirrors and containing a gashaving a chemical species to be measured, a laser optically coupled tothe resonant optical cavity, and a detector system for measuringabsorption of laser light by the gas in the cavity.

According to another embodiment, a gas analyzer system is provided formeasuring an isotopic ratio gas species. The system typically includes agas cell containing a gas to be measured, a laser optically coupled tothe cell, and a detector system for measuring the laser lighttransmitted through the cell.

According to another embodiment, a gas analyzer system is provided formeasuring an isotopic ratio of gas species. The system typicallyincludes an optical cavity containing a gas having a chemical species tobe measured, a laser optically coupled to the optical cavity, and adetector system for measuring absorption of laser light by the gas inthe cavity. In certain aspects, the gas analyzer system utilizes thecavity ring-down spectroscopy method to measure absorption of the laserlight by the gas in the cavity.

According to another embodiment, a gas analyzer system is provided formeasuring an isotopic ratio of gas species. The system typicallyincludes an optical cavity containing a gas having a chemical species tobe measured, a laser optically coupled to the optical cavity, and adetector system for measuring absorption of laser light by the gas inthe cavity. In certain aspects, the gas analyzer system utilizes thephase shift spectroscopy method to measure absorption of the laser lightby the gas in the cavity.

According to another embodiment, a gas analyzer system is provided formeasuring an isotopic ratio of gas species. The system typicallyincludes an optical cavity containing a gas having a chemical species tobe measured, a laser optically coupled to the optical cavity, and adetector system for measuring absorption of laser light by the gas inthe cavity. In certain aspects, the gas analyzer system utilizes thecavity enhanced absorption spectroscopy method to measure absorption ofthe laser light by the gas in the cavity.

According to another embodiment, a gas analyzer system is provided formeasuring an isotopic ratio of gas species. The system typicallyincludes an optical cavity containing a gas having a chemical species tobe measured, a laser optically coupled to the optical cavity, and adetector system for measuring absorption of laser light by the gas inthe cavity. In certain aspects, the gas analyzer system utilizes thephotoacoustic spectroscopy method to measure absorption of the laserlight by the gas in the cavity.

According to another embodiment, a gas analyzer system is provided formeasuring an isotopic ratio of gas species. The system typicallyincludes an optical cavity containing a gas having a chemical species tobe measured, a laser optically coupled to the optical cavity, and adetector system for measuring absorption of laser light by the gas inthe cavity. In certain aspects, the gas analyzer system utilizes thetunable diode lasers spectroscopy method to measure absorption of thelaser light by the gas in the cavity.

According to another embodiment, a gas analyzer system is provided formeasuring an isotopic ratio of gas species. The system typicallyincludes an optical cavity containing a gas having a chemical species tobe measured, a laser optically coupled to the optical cavity, and adetector system for measuring absorption of laser light by the gas inthe cavity. In certain aspects, the gas analyzer system also includes atemperature sensor for measuring the temperature of the gas in thecavity, and a pressure sensor for measuring the pressure of the gas inthe cavity. In certain aspects, the detector system includes one of aphoto-detector configured to measure an intensity of the intra-cavitylight or both a photo-acoustic sensor configured to measurephoto-acoustic waves generated in the cavity and a photo-detectorconfigured to measure an intensity of the intra-cavity light.

According to yet another embodiment, a gas analyzer system is providedfor measuring an isotopic ratio gas species. The system typicallyincludes an optical cavity containing a gas having a chemical species tobe measured, a laser optically coupled to the optical cavity, and adetector system for measuring the absorption of laser light by the gasin the cavity. In certain aspects, the gas analyzer system also includesa control element configured to control temperature of the gas in theoptical cavity and a pressure control element configured to controlpressure of the gas in the optical cavity.

All references, including publications, patent applications, andpatents, cited herein are hereby incorporated by reference to the sameextent as if each reference were individually and specifically indicatedto be incorporated by reference and were set forth in its entiretyherein.

The use of the terms “a” and “an” and “the” and “at least one” andsimilar referents in the context of describing the disclosed subjectmatter (especially in the context of the following claims) are to beconstrued to cover both the singular and the plural, unless otherwiseindicated herein or clearly contradicted by context. The use of the term“at least one” followed by a list of one or more items (for example, “atleast one of A and B”) is to be construed to mean one item selected fromthe listed items (A or B) or any combination of two or more of thelisted items (A and B), unless otherwise indicated herein or clearlycontradicted by context. The terms “comprising,” “having,” “including,”and “containing” are to be construed as open-ended terms (i.e., meaning“including, but not limited to,”) unless otherwise noted. Recitation ofranges of values herein are merely intended to serve as a shorthandmethod of referring individually to each separate value falling withinthe range, unless otherwise indicated herein, and each separate value isincorporated into the specification as if it were individually recitedherein. All methods described herein can be performed in any suitableorder unless otherwise indicated herein or otherwise clearlycontradicted by context. The use of any and all examples, or examplelanguage (e.g., “such as”) provided herein, is intended merely to betterilluminate the disclosed subject matter and does not pose a limitationon the scope of the invention unless otherwise claimed. No language inthe specification should be construed as indicating any non-claimedelement as essential to the practice of the invention.

Certain embodiments are described herein. Variations of thoseembodiments may become apparent to those of ordinary skill in the artupon reading the foregoing description. The inventors expect skilledartisans to employ such variations as appropriate, and the inventorsintend for the embodiments to be practiced otherwise than asspecifically described herein.

The invention claimed is:
 1. A gas analyzer system for measuring anisotopic ratio of a gaseous chemical species by an optical absorptionspectroscopy method, the system comprises: an optical cavity containinga gas with the chemical species to be measured; a laser opticallycoupled to an optical cavity; a detector system for measuring absorptionof laser light by the gas; and an intelligence module comprising aprocessor adapted to determine a concentration ratio of two differentisotopologues, wherein rotational-vibrational spectra of the chemicalspecies are measured at least within two non-overlapping spectralintervals separated by a minimum of 50 nm between any two spectralpoints from each of the spectral intervals and selected in such a waythat a first rotational-vibrational line of a firstrotational-vibrational band of a less abundant isotopologue is locatedin a first spectral interval, and a second rotational-vibrational lineof a second rotational-vibrational band of a more abundant isotopologueis located in a second spectral interval, and a line intensity of thestrongest line of the first rotational-vibrational band of the lessabundant isotopologue is two or more times stronger than a lineintensity of the strongest line of the second rotational-vibrationalband of the more abundant isotopologue, and a ratio of an absorptionspectrum of the less abundant isotopologue to the sum of absorptionspectra of all other isotopologues of the chemical species weighted bymole-fraction abundance figures exceeds two somewhere in the firstspectral interval, and a ratio of an absorption spectrum of the moreabundant isotopologue to the sum of absorption spectra of all otherisotopologues of the chemical species weighted by mole-fractionabundance figures exceeds two somewhere in the second spectral interval.2. The system of claim 1, wherein the pressure broadening coefficientsof the first line and the second line are different by no more than 50%.3. The system of claim 1, wherein the temperature dependencecoefficients of the first line and the second line are different by nomore than 50%.
 4. The system of claim 1, wherein the optical absorptionspectroscopy method comprising of at least one of the following methods:the cavity ring down spectroscopy method, the cavity enhanced absorptionspectroscopy method, the cavity phase shift spectroscopy method, theintegrated cavity output spectroscopy method, or the cavity enhancedphoto-acoustic spectroscopy method.
 5. The system of claim 1, whereinthe optical cavity is a resonant optical cavity.
 6. The system of claim1, wherein the detector system includes one of a photo-detectorconfigured to measure an intensity of the intra-cavity light or both aphoto-acoustic sensor configured to measure photo-acoustic wavesgenerated in the cavity and a photo-detector configured to measure anintensity of the intra-cavity light.
 7. The system of claim 1, whereinone of the measured isotopologues is ¹⁶O¹³C¹⁶O and another measuredisotopologue is ¹⁶O¹²C¹⁶O.
 8. The system of claim 1, further comprisinga temperature sensor for measuring a temperature of the gas in theoptical cavity; and a pressure sensor for measuring a pressure of thegas in the optical cavity.
 9. The system of claim 8, further comprisinga temperature control element configured to control a temperature of thegas in the optical cavity and a pressure control element configured tocontrol a pressure of the gas in the optical cavity.
 10. A gas analyzersystem for measuring an isotopic ratio of a gaseous chemical species byan optical absorption spectroscopy method, the system comprises: anoptical cell containing a gas with the chemical species to be measured;a laser configured to emit light into an optical cell; a detector systemfor measuring absorption of laser light by the gas; and an intelligencemodule comprising a processor adapted to determine a concentration ratioof two different isotopologues, wherein rotational-vibrational spectraof the chemical species are measured at least within two non-overlappingspectral intervals separated by a minimum of 50 nm between any twospectral points from each of the spectral intervals and selected in sucha way that a first rotational-vibrational line of a firstrotational-vibrational band of a less abundant isotopologue is locatedin a first spectral interval, and a second rotational-vibrational linesof a second rotational-vibrational band of a more abundant isotopologueis located in a second spectral interval, and a line intensity of thestrongest line of the first rotational-vibrational band of the lessabundant isotopologue is two or more times stronger than a lineintensity of the strongest line of the second rotational-vibrationalband of the more abundant isotopologue, and a ratio of an absorptionspectrum of the less abundant isotopologue to the sum of absorptionspectra of all other isotopologues of the chemical species weighted bymole-fraction abundance figures exceeds two somewhere in the firstspectral interval, and a ratio of an absorption spectrum of the moreabundant isotopologue to the sum of absorption spectra of all otherisotopologues of the chemical species weighted by mole-fractionabundance figures exceeds two somewhere in the second spectral interval.11. A method of measuring an isotopic ratio of a gaseous chemicalspecies, the method comprising: coupling laser light to an opticalcavity containing a gas with the chemical species to be measured;measuring an absorption of the laser light by the gas; determining theconcentration ratio of two different isotopologues, whereinrotational-vibrational spectra of the chemical species are measured atleast within two non-overlapping spectral intervals separated by aminimum of 50 nm between any two spectral points from each of thespectral intervals and selected in such way that a firstrotational-vibrational line of a first rotational-vibrational band of aless abundant isotopologue is located in a first spectral interval, anda second rotational-vibrational line of a second rotational-vibrationalband of a more abundant isotopologue is located in a second spectralinterval, and a line intensity of the strongest line of the firstrotational-vibrational band of the less abundant isotopologue is two ormore times stronger than a line intensity of the strongest line of thesecond rotational-vibrational band of the more abundant isotopologue,and a ratio of an absorption spectrum of the less abundant isotopologueto the sum of absorption spectra of all other isotopologues of thechemical species weighted by mole-fraction abundance figures exceeds twosomewhere in the first spectral interval, and a ratio of an absorptionspectrum of the more abundant isotopologue to the sum of absorptionspectra of all other isotopoloques of the chemical species weighted bymole-fraction abundance figures exceeds two somewhere in the secondspectral interval.
 12. The method of claim 11, wherein the pressurebroadening coefficients of the first line and the second line aredifferent by no more than 50%.
 13. The method of claim 11, wherein thetemperature dependence coefficients of the first line and the secondline are different by no more than 50%.
 14. The method of claim 11,wherein the optical absorption spectroscopy method comprising at leastone of the following methods: the cavity ring down spectroscopy method,the cavity enhanced absorption spectroscopy method, the cavity phaseshift spectroscopy method, the integrated cavity output spectroscopymethod, or the cavity enhanced photo-acoustic spectroscopy method. 15.The method of claim 11, wherein the optical cavity is a resonant opticalcavity.
 16. The method of claim 11, wherein one of the measuredisotopologues is ¹³C¹⁶O₂ and another measured isotopologue is ¹²C¹⁶O₂.17. The method of claim 11, further comprising: measuring a temperatureof the gas in the optical cavity by a temperature sensor and measuring apressure of the gas in the optical cavity by a pressure sensor.
 18. Themethod of claim 17, further comprising: controlling a temperature of thegas in the optical cavity by a temperature control element andcontrolling a pressure of the gas in the optical cavity by a pressurecontrol element.